He said: “How can we build trust and start discussing the future relationship? We have to address these things together seriously.”

Barnier also warned that the integrity of the single market would not be risked by Brexit.

He said: “The UK wants to take back control, wants to adopt its own standards and regulations – but it also wants to have these standards recognised automatically in the EU.

“That is what UK papers ask for. This is simply impossible. You cannot be outside the single market and shape its legal order.”

He added: “The current state of progress means we are quite far from being able to say sufficient progress has taken place, not far enough for me to be able to say to the European council that we can start to discuss the future relationship.”

Davis was more positive, saying: “I think we have succeeded in building mutual understanding, but it is also clear that there are still significant differences to be bridged.”

Commenting after the press conference, Shadow Brexit secretary Keir Starmer said the danger of the UK crashing out of the EU was “now very real.”

He said: “After three rounds of negotiations, real progress should have been made and in principle agreements reached on all phase one issues. Instead, the two sides appear to be getting further apart.

“The risk of not reaching the October deadline to move on to the main negotiations is now very real; which increases the risk of Britain leaving with “no deal” in March 2019.

“No deal would be the worst possible outcome for the British people.

“Both sides need to redouble efforts and work together to reach a strong Article 50 deal and a close future partnership.

“If more negotiating sessions need to be added between now and the October deadline, they should be. Substantive progress and clear outcomes are urgently needed.”